SOLUTION: an art museum charges $10 for an adult admission. The museum estimates they will lose 15 adult visitors per day for each one dollar increase in price. If the museum averages 300

Question 453695: an art museum charges $10 for an adult admission. The museum estimates they will lose 15 adult visitors per day for each one dollar increase in price. If the museum averages 300 adult visitors a day, which is the most profitable adult admission price?
Found 2 solutions by htmentor, josmiceli:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
an art museum charges $10 for an adult admission. The museum estimates they will lose 15 adult visitors per day for each one dollar increase in price. If the museum averages 300 adult visitors a day, which is the most profitable adult admission price?
Let x = the admission price
Then the number of visitors will be 300 - 15(x-10) [300 for x=10, 285 for x=11, etc.]
The total revenue will be:
R = x(300 - 15(x-10))
R = 300x - 15x^2 + 150x
R = 450x - 15x^2
To maximize the profit, we set dR/dx = 0 and solve for x:
dR/dx = 0 = 450 - 30x
This gives x = 15
So the most profitable price is $15
The graph of the revenue function is below:

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = money taken in
Let = number of $1 increases
Money in = (number of adult visitors) x (admission per visitor)

The maximum money in occurs at
where the equation has the form

The most profitable admission price is $15/visitor
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